measuremen ts of angular distributions of muons from upsilon meson decays in collisions at 1 96 tev n.
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Measuremen ts of Angular Distributions of Muons From Upsilon Meson Decays in Collisions at =1.96 TeV. To be submitted to PRL. Matthew Jones Purdue University. Some very old results…. Phys. Rev. Lett . 75 , 4358 (1995). Phys. Rev. Lett. 79, 572 (1997).

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measuremen ts of angular distributions of muons from upsilon meson decays in collisions at 1 96 tev

Measurements of Angular Distributions of Muons From Upsilon Meson Decays in Collisions at =1.96 TeV

To be submitted to PRL

Matthew Jones

Purdue University

CDF Weekly Meeting Paper Seminar

slide2

Some very old results…

Phys. Rev. Lett. 75, 4358 (1995)

Phys. Rev. Lett. 79, 572 (1997)

  • Prompt J/ψ and ϒ cross sections much larger than expected…

color-singlet vs color-octet production mechanisms

Polarization measurements

Direct + feed-down from decays

Direct

CDF Weekly Meeting Paper Seminar

upsilon polarization
Upsilon “Polarization”
  • A better term is spin alignment…
    • Transverse polarization:
    • Longitudinal polarization:

μ+

θ*

ϒ momentum

μ-

(this is called the s-channel helicity frame)

CDF Weekly Meeting Paper Seminar

recent status
Recent Status
  • CDF found no evidence for polarization in Run I Phys. Rev. Lett. 88, 161802 (2002).
  • DØ finds it to be longitudinal at low pT, then transverse at high pTPhys. Rev. Lett. 101, 182004 (2008).
  • Models:
    • NRQCD – Braaten & Lee, Phys. Rev. D63, 071501(R) (2001)
    • kT – Baranov & Zotov, JETP Lett. 86, 435 (2007)
  • Newer NLO calculations show similar trends:
    • NLO NRQCD – Gong, Wang & Zhang, Phys. Rev. D83, 114021 (2011)
    • Color singlet NNLO* - Artoisenent, et al. Phys. Rev. Lett. 101, 152001 (2008)

CDF Weekly Meeting Paper Seminar

new old analysis paradigm
New (old) analysis paradigm
  • The current situation is unsatisfactory... are we missing something obvious?
  • Back to the fundamentals:
  • Un-polarized only when λθ, λφ and λθφ are all zero.
  • Compare rotational invariant in different reference frames:

s-channel helicity frame and Collins-Soper frame

PietroFaccioliemphasizes basic quantum mechanics...

CDF Weekly Meeting Paper Seminar

new cdf analysis 6 7 fb 1
New CDF Analysis – 6.7 fb-1
  • Goals:
    • Measure all three parameters simultaneously
    • Measure in Collins-Soper and S-channel helicity frame
    • Test self-consistency by calculating rotationally invariant combinations of λθ, λφ and λθφ
    • Provide first measurements on the ϒ(3S) state
  • Concerns based on past experience at CDF:
    • Minimize sensitivity to modeling the ϒ(nS) resonance line shape
    • Explicit measurement of angular distribution of dimuon background

Public note: CDF/PUB/BOTTOM/PUBLIC/10665

CDF Weekly Meeting Paper Seminar

analysis method
Analysis Method
  • Reconstruct μ+μ- candidates, boost into rest frame, calculate decay angles (cosθ,φ)
  • Observed distribution depends on acceptance and the underlying angular distribution:
    • A(cosθ,φ) from high statistics Monte Carlo
    • w(cosθ,φ; λθ, λφ,λθφ ) from angular distribution formula
  • Performed binned likelihood fit to observed distribution of (cosθ,φ) to determine λθ, λφ,λθφ.
  • But there is background…

CDF Weekly Meeting Paper Seminar

analysis method1
Analysis Method
  • Both signal and background are present
  • Conceptual problem:
  • Signal fraction obtained from fit to mass distribution
  • How to constrain angular distribution of the background?
  • Side-band extrapolation?
    • Does it vary smoothly enough?
    • Probably not…

Geometric and trigger acceptance calculated using Monte Carlo

CDF Weekly Meeting Paper Seminar

new approach
New Approach
  • Use muon impact parameter to isolate a background-enhanced (displaced) sample
    • Complimentary sample (prompt) contains most of the ϒ(nS) signal.
    • Impact parameter requirement must not bias angular distributions:
    • Require (at least) one muon to have |d0| > 150 μm
  • Fit to displaced sample + prompt sidebands:
    • Measures ratio of prompt/displaced backgrounds
    • Scale displaced sample to predict background level under the ϒ(nS)
  • Two component fit to (cosθ,φ) distribution
    • Determines λθ, λφ,λθφfor signal and background
    • Background parameterization is purely emperical; an additional term is helpful

CDF Weekly Meeting Paper Seminar

background proxy sample
Background Proxy Sample

Prompt, |d0| < 150 μm

Displaced, |d0| > 150 μm

Small fraction of the ϒ signal is still present in the displaced sample (1-4%)

The ratio of prompt/secondary distributions is almost constant.

Simultaneous fit to displaced sample and ϒsidebands avoids possible bias from modeling theϒ line shape.

Quadratic scale factor function considered in systematic studies

m(μ+μ- ) (GeV/c2)

m(μ+μ- ) (GeV/c2)

CDF Weekly Meeting Paper Seminar

angular distributions in sidebands
Angular distributions in sidebands
  • The sub-sample containing a displaced track (|d0| > 150 μm) is a good description of the background under the ϒ(nS):
  • Prompt (histogram) and displaced (error bars) angular distributions match in the sidebands.
  • We use the displaced muon sample to constrain the angular distribution of background under the ϒ(nS) peaks.

φ (deg)

φ (deg)

cosθ

cosθ

Low-mass sideband

High-mass sideband

CDF Weekly Meeting Paper Seminar

fits to signal background
Fits to signal + background
  • The fit provides a good description of the angular distribution in both background and in signal + background mass bins.

Only background

φ (deg)

cosθ

ϒ(1S) signal + background

φ (deg)

cosθ

CDF Weekly Meeting Paper Seminar

frame invariance tests
Frame Invariance Tests
  • Differences generally consistent with size of statistical fluctuations seen in toy Monte Carlo experiments
    • Differences used to quantify systematic uncertainties on λθ, λφ and λθφ

ϒ(1S)

ϒ(2S)

ϒ(3S)

Collins-Soper

s-channel helicity

ϒ(3S) pT (GeV/c)

ϒ(2S) pT (GeV/c)

ϒ(1S) pT (GeV/c)

CDF Weekly Meeting Paper Seminar

comparison with previous measurements
Comparison with Previous Measurements

Run I CDF result

Run II DØ result

New ϒ(1S) result

CDF Weekly Meeting Paper Seminar

comparisons with newer calculations
Comparisons with newer calculations

CDF Run II preliminary – 6.7 fb-1

Nucl. Phys. B 214, 3 (2011) summary:

  • NLO NRQCD – Gong, Wang & Zhang, Phys. Rev. D83, 114021 (2011)
  • Color-singlet NLO and NNLO* - Artoisenent, et al. Phys. Rev. Lett. 101, 152001 (2008)

NLO NRQCD with color-octet matrix elements

Significant uncertainty due to feed-down from χb(nP) states (conservative assumptions)

NLO color- singlet

CDF Weekly Meeting Paper Seminar

table of results
Table of Results
  • No evidence for strong longitudinal or transverse polarization, even for the ϒ(3S) state.
  • Other fitted parameters to be made available as supplemental material on PRL web site.

CDF Weekly Meeting Paper Seminar

summary
Summary
  • First complete measurement of angular distribution of ϒ(nS) decays at a hadron collider.
  • First measurement of ϒ(3S) spin alignment.
  • No evidence for significant polarization*
    • Even up to pT of 40 GeV/c
    • Even for the ϒ(3S)

* In the central region of rapidity, |y|<0.6

CDF Weekly Meeting Paper Seminar